Cindi,
I had something similar in a previous house. A supply pipe to a loft tank would habitually burst in really cold weather despite it being properly insulated.
A fool had put insulation under the tank - cold wind would blow up the overflow pipe and ice would form in the tank.
The brass inlet valve on the tank acted as a heat exchanger and drew all the heat from the lagged pipe that delivered the water - the lagged supply pipe would burst. The insulation on this pipe actually made things worse!
Examine the device that the worrying pipe connects to - the cold may be coming from there...
Good luck...
Peccavi
January 2009